Generally, no. Unless, of course, that NY big firm also has an office in your area.

check nalpdirectory.com to see which firms will interview at your school. Most NYC firms interview at nearly all of the New York schools. But outside of NYC and Rutgers, you can probably guess with which schools they all interview.

If you do outstanding in your first year (probably top 10%, but don't take that as dogma), you can write directly to the law firms that don't interview at your school.